Study on $$\Xi _{cc}\rightarrow \Xi _c$$ and $$\Xi _{cc}\rightarrow \Xi '_c$$ weak decays in the light-front quark model
Hong-Wei Ke, Fang Lu, Xiao-Hai Liu, Xue-Qian Li
Abstract
Abstract In this work we study the weak decays of $$\Xi _{cc}\rightarrow \Xi _c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ξ</mml:mi><mml:mrow><mml:mi>cc</mml:mi></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mi>Ξ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math> and $$\Xi _{cc}\rightarrow \Xi '_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ξ</mml:mi><mml:mrow><mml:mi>cc</mml:mi></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>c</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math> in the light-front quark model. Generally, a naive, but reasonable conjecture suggests that the cc subsystem in $$\Xi _{cc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Ξ</mml:mi><mml:mrow><mml:mi>cc</mml:mi></mml:mrow></mml:msub></mml:math> ( us pair in $$\Xi ^{(')}_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:msup><mml:mo>(</mml:mo><mml:mo>′</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:msubsup></mml:math> ) stands as a diquark with definite spin and color assignments. During the concerned processes, the diquark of the initial state is not a spectator, namely must be broken. A Racah transformation would decompose the original ( cc ) q into a combination of c ( cq ) components. Thus we may deal with the decaying c quark alone while keeping the ( cq ) subsystem as a spectator. With the re-arrangement of the inner structure we calculate the form factors numerically and then obtain the rates of semi-leptonic decays and non-leptonic decays, which will be measured in the future.